Torsion of abelian varieties over large algebraic fields

We prove: Let A be an abelian variety over a number field K. Then K has a finite Galois extension L such that for almost all σ Gal(L) there are infinitely many prime numbers l with . Here denotes the algebraic closure of K and the fixed field in of σ. The expression “almost all σ” means “all but a set of σ of Haar measure 0”.